Optimal Voting Strategies for “The Weakest Link”

The television program “The Weakest Link,” is a game show with a winner-take-all format in which players vote to remove potential rivals following each round. The obvious question is whether or not the title of the show indicates the optimal strategy for a player to follow. To make a mathematical model tractable, I consider a game with only three players and replace the time limit with a question limit. I have also chosen a simpler “banking” strategy than the one used on the program. Expected payoffs are calculated as a function of each player’s probability of answering correctly, as well as the order in which players are eliminated.

Not surprisingly, the strategy implied by the title of the show is, in many cases, not the optimal one. A qualitative description of the optimal strategy will be given. In addition, suggestions on how to extend the analysis to more than three players will be given.